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## Homework Statement

([tex]\sqrt{(n+1)}[/tex] - [tex]\sqrt{n}[/tex] ) [tex]/[/tex] [tex]\sqrt{n}[/tex]

I'm trying to show this series converges.

## Homework Equations

divergence test: as n approaches infinity, if the sequence does not approach 0 then the series diverges

ratio test: as n approaches infinity, if the ratio between subsequent terms is less than 1 then the series converges, if equal to 1 the test is inconclusive, if greater than 1 then the series diverges

comparison test: if this series is smaller than another series that converges, then this series also converges; if this series is greater than another series that diverges, then this series also diverges

## The Attempt at a Solution

Applying the divergence test, the sequence definitely approaches 0, but this cannot be used to prove convergence

I tried using ratio test (which has worked so well for nearly every question) and ended up with a mess of square roots.

I'm thinking of using comparison test, but what series can I compare it to?